Overlap Coefficients Research Articles

Abstract P3-03-13: Testing algorithmic basis for combinations of targeted drugs by a mechanism-based laboratory friendly identification of apoptosis in live breast cancer cells

Abstract Background: The mechanism of induction of apoptosis has been one of the features to characterize and classify anti-tumor drugs. We have standardized a mechanism-based approach to identify apoptosis in live tumor cells by triple co-fluorescence (De et al., 2018; SCIENTIFIC REPORTS). Our protocol tests three crucial features of apoptosis; the enzymatic activity of executioner caspase3, cell surface presentation of caspase-dependent phosphatidylserine and mitochondrial function. Navigating the genomic landscape of tumors in patients with Triple Negative Breast Cancers (TNBC) at Avera Cancer Institute, we have identified algorithm for the rational combination of PI3K-pathway (PP) drugs. Aim: Here we present the results of testing the rational combinations of PP-targeted drugs on apoptosis using our mechanism-based laboratory friendly procedure. Methods: Our protocol co-stains live tumor cells in real time with NucView488 Casp3substrate (N), CF594AnnexinV (A), and MitoViewBlue (M). We have used carboplatin and targeted-drugs like olaparib, ABT888, BMN673, AZD2014, GDC0980, and AZD5363 in BRCA-WT (MDA-MB231, MDA-MB468) and BRCA-incompetent (SUM149) TNBC cells. Imaging of cells using simultaneous live/dead cell markers (Calcein AM green/EthD-1 red) was used for validation. Results: We retrospectively analyzed genomic data [FoundationOne] from 100 consecutive patients seen in our center from 2014. 137 genes were altered including 12 PP and 11 DNA-repair genes. We used AnnexinV-PE staining (Accuri C6), confocal IF imaging and WB expression of apoptotic signals and mitochondrial potential (TMRE-A) as validation criteria following different combinations. Treatment with the rational combination(s) like PARP inhibitor(s) plus carboplatin and PP inhibitor decreased proliferation, induced profound early apoptotic events, along with increased apoptotic signaling and increased mitochondrial depolarization in real time. Dual treatment also blocked cytoplasmic M staining while increasing both nuclear N substrate staining and membranous A staining. Control cells had higher Calcein AM positive (live) cells and fewer EthdD-1 stained red nuclei of dead cells than treated cells. Merged images (M+N+A) showed 100% mutual exclusivity between M and N or A stains in both control and treated cells as determined by overlap and colocalization coefficients. Conclusion: Our method of staining identified the apoptosis following treatment of drug-combination(s), which was based on the genomic alteration(s) present in TNBC patients. Citation Format: Nandini Dey, Jennifer Carlson Aske, Pradip De. Testing algorithmic basis for combinations of targeted drugs by a mechanism-based laboratory friendly identification of apoptosis in live breast cancer cells [abstract]. In: Proceedings of the 2019 San Antonio Breast Cancer Symposium; 2019 Dec 10-14; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2020;80(4 Suppl):Abstract nr P3-03-13.

Experimental definition of rational modes of shock-acoustic treatment

The paper presents the results of experimental studies to determine the rational technological parameters of shock-acoustic treatment (SAT) in order to provide the best antifriction properties for the outer surfaces of parts made of Steel 45. On the basis of experimentally selected processing modes, the specified values of overlap coefficients for the ultrasonic instrument and workpiece contact areas are determined. The use of shock-acoustic treatment with simultaneous application of a solid lubricant coating allows the surface microhardness to be increased almost by the factor of two and the roughness to be reduced to Ra 0.2.

Distribution of psychological distress is stable in recent decades and follows an exponential pattern in the US population

The prevalence of psychological distress is fairly stable in industrialised countries in recent decades, but the reasons for this stability remain unknown. To investigate the mechanisms underlying stability of psychological distress in the general population of the United States, we analysed the mathematical patterns of the distribution of psychological distress in recent decades. The present study utilised the Kessler psychological distress scale (K6) data from the 1997‒2017 United States National Health Interview Survey. We used overlap coefficients and graphical analysis to investigate the stability and mathematical patterns of the K6 distribution. Overlap coefficients and graphical analysis demonstrated that the distribution of K6 total scores was stable in the United States over the past two decades. Furthermore, the distributions of K6 total scores exhibited an exponential pattern, with the exception of the lower end of the distribution. These findings suggest that the lack of change in the prevalence of psychological distress over several decades is due to the stability of psychological distress distribution itself. Furthermore, the stability of the distribution of psychological distress over time may be linked to the exponential pattern of psychological distress distribution.

Stimulation of the Tractography-Defined Subthalamic Nucleus Regions Correlates With Clinical Outcomes.

Although deep brain stimulation (DBS) of the dorsolateral subthalamic nucleus (STN) is a well-established surgical treatment for patients with Parkinson disease (PD), there is still controversy about the relationship between the functional segregation of the STN and clinical outcomes. To correlate motor and neuropsychological (NPS) outcomes with the overlap between the volume of activated tissue (VAT) and the tractography-defined regions within the STN. Retrospective study evaluating 13 patients with PD treated with STN-DBS. With the aid of tractography, the STN was segmented into 4 regions: smaSTN (supplementary motor area STN), m1STN (primary motor area STN), mSTN (the sum of the m1STN and the smaSTN segments), and nmSTN (non-motor STN). We computed the overlap coefficients between these STN regions and the patient-specific VAT. The VAT outside of the STN was also calculated. These coefficients were then correlated with motor (Unified Parkinson's Disease Rating Scale, UPDRS III) and NPS outcomes. Stimulation of the mSTN segment was significantly correlated with UPDRS III and bradykinesia improvement. Stimulation of the smaSTN segment, but not the m1STN one, had a positive correlation with bradykinesia improvement. Stimulation of the nmSTN segment was negatively correlated with the improvement in rigidity. Stimulation outside of the STN was correlated with some beneficial NPS effects. Stimulation of the tractography-defined motor STN, mainly the smaSTN segment, is positively correlated with motor outcomes, whereas stimulation of the nmSTN is correlated with poor motor outcomes. Further validation of these results might help individualize and optimize targets prior to STN-DBS.

Abstract 718: A laboratory friendly visualization method of triple-co-fluorescence staining to identify cytomorphological features of apoptosis simultaneously with biochemical events in live cells

Abstract Background: During apoptosis, its cytomorphological features are functionally coupled to its tightly regulated and ATP-dependent biochemical events. Traditionally, identification and quantification of apoptosis in the laboratory are based on one of these features at a time from either lysed or fixed cells. Aim: We present a protocol for staining live cells in a culture undergoing apoptosis in real-time. Live cell-imaging by Triple-co-Fluorescent Staining (TFS) is standardized to test 3 crucial events of apoptosis simultaneously in a single cell; the enzymatic activity of executioner caspase3, caspase-dependent phosphatidylserine presentation on cell-surface and mitochondrial depolarization. Methods: Live cells were stained simultaneously with the NucView488-Casp3 substrate (G), CF594 AnnexinV (R), and MitoViewBlue (B). Specificity of the staining was tested by co-localization & caspase3 inhibitor assay. We used (1) real-time confluency (Incucyte), (2) Annexin V (Accuri C6), (3) WB expression of cl-caspase3, cl-PARP, and BIM, and (4) TMRE-A based mitochondrial depolarization on validating our method. CalceinAM green and EthD-1red were used as internal staining controls. This method was verified to test combinations of chemotherapy and targeted therapy drugs in tumor cells. Results: Drug combinations blocked cytoplasmic B staining while increased both G & R staining compared to controls. Merged images showed 100% mutual exclusivity between B & G stains in control and treated cells as determined by overlap and co-localization coefficients. Pixel co-localization between FITC (G and CalceinAM), DAPI (B) and TRITC (R and EthD-1) channels from 2.5 nM paclitaxel + 500 nM BKM120 or paclitaxel only treated OVK18 cells confirmed above results. Caspase3 and AnnexinV staining in treated cells, however, were both separate and overlapped (yellow fluorescence) indicating the sequence of apoptotic-events. Co-localization between FITC, DAPI, and TRITC channels was determined in the scatterplot of merged channels. No co-localization between EthD-1 red and CalceinAM green cells was observed. Ac-DEVD-CHO, a tetrapeptide (amino acid sequence of PARP cleavage site) that acts as a competitive inhibitor for caspase-3/7 was used to test the specificity of the assay. Significance: The strength of our method lies in our (a) choice of TFS, (b) independent validations, and (c) specificity of staining. To the best our knowledge this is the most stringent method to visualize 3 critical features of apoptosis simultaneously and conclusively deciphering mechanistic involvement of different stages/features of apoptosis in live tumor cells in real-time which can be applied in live tumor cells to test chemotherapy and targeted drugs’ efficacy in everyday laboratory practice with the help of a minimalistic laboratory setup. Citation Format: Brian R. Leyland-Jones, Jennifer H. Aske, Pradip De, Nandini Dey. A laboratory friendly visualization method of triple-co-fluorescence staining to identify cytomorphological features of apoptosis simultaneously with biochemical events in live cells [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 718.

Assessing caracal-prey interactions by spatial and temporal analyses

In this study, we assessed habitat preferences and temporal activity patterns of caracal (Caracal caracal) and several possible prey species in Koycegiz Wildlife Development Reserve, south-western Turkey. We investigated whether wild goat (Capra aegagrus) is indeed the main prey of caracal and if there is evidence for excessive caracal predation on this ungulate as previously stated by researchers, wildlife wardens and hunters. Results of this 2249 camera trap-day survey revealed a high habitat segregation between caracal and wild goat (Pianka’s O = 0.2) and very high overlap between caracal and other prey species such as brown hare (Lepus europaeus), field mice (Apodemus spp.), chukar partridge (Alectoris chukar) and wild boar (Sus scrofa) (Pianka’s O = 0.8–1.0). Wild goats preferred steep slopes (Chesson’s α = 0.85) and associated narrow valley bottoms, whereas caracals preferred high flatland forests (Chesson’s α = 0.95). The overlap coefficients in temporal activity patterns of caracal and wild goat (Δ1 = 0.50), and caracal and other prey species were moderate (Δ1 = 0.40–0.59), and did not indicate strict predator-prey relationships based on temporal activities. The results of this study do not support a caracal diet based mainly on wild goat, due to their mostly spatial and partially temporal segregation. Other smaller prey species such as brown hare, rodents and chukar partridge can serve as better prey options due to their continuous presence in caracal habitat throughout the day and year.

Overlap Coefficients Based on Kullback-Leibler of Two Normal Densities: Equal Means Case

Overlap coefficient (OVL) represents the proportion of overlap between two probability distributions, as a measure of the similarity between them. In this paper, we define a new overlap coefficient Λ based on Kullback-Leibler divergence and compare its performance to three known overlap coefficients, namely Matusia's Measure, Morisita's Measure, Weitzman's Measure. We study their properties, relations between them, and give approximate expressions for the biases and the variances.

Detection of particle position from a linear interferometric out-of-focus image

A high precision method based on erosion match is proposed to extract the location coordinate of particles from a compression interferogram. With this method, particles can be positioned exactly when the overlap coefficients for that perpendicular and parallel to the fringes are less than 94.23% and 25% respectively. Super performance with the method is well confirmed by the synthetic and experiment data. Furthermore, the method can also be employed in the center detecting of complex fringe patterns for both circular and linear fringe images. The numerical and experimental results suggest that the method presented may be of considerable value to high-density spray field in accurately measuring both the particle location and its velocity.

Stable isotope patterns reveal widespread rainy-period-biased recharge in phreatic aquifers across Greece

The stable isotopic composition of water (δ18O, δ2H) is used to trace different components of the hydrological cycle, particularly interactions between precipitation, surface, and ground water. In Greece, insufficient spatial coverage for isotopes in precipitation hinders investigations of relationship between ground water and precipitation, information that is required to help quantify aquifer replenishment rates. We used precipitation, geospatial, ground water isotope data and General Linear Models (GLM) to predict the spatial distribution of isotopes in phreatic ground water in Greece. Prediction covariates of elevation, latitude, distance to nearest coastline, drainage basin (western vs. eastern Greece), and amount of precipitation predicted 62% of the isotopic variance in ground water. The GLM model yielded predictions of the isotopic composition of shallow aquifers, which allowed us to construct maps for use in hydrological and other forensic applications in Greece. A comparison of the stable isotope values predicted by our GLM to those of existing precipitation models revealed that phreatic aquifers in Greece are mainly recharged during the annual wet period, between November and March, as documented by the high overlap coefficients of 0.77 and 0.82, respectively. Rainy-period-biased aquifer recharge has implications for water quality and management issues, for example, nitrate pollution may be enhanced in the non-growing rainy period when crop uptake is the lowest, or for water resource management if climatic changes alter these temporal rainfall patterns.

Triple Fluorescence staining to Evaluate Mechanism-based Apoptosis following Chemotherapeutic and Targeted Anti-cancer Drugs in Live Tumor Cells

We present a protocol for live cancer cell-imaging by triple-fluorescent staining to test 3 crucial mechanisms of apoptosis; the enzymatic activity of executioner caspase3, caspase-dependent phosphatidylserine presentation on the cell surface and mitochondrial function. We standardized a protocol to co-stain live tumor cells with the NucView488-Casp3 substrate, CF594 AnnexinV, and MitoViewBlue. We validated this protocol following apoptosis induction with paclitaxel or in combination with BKM120. Fluorescent imaging of cells using simultaneous live/dead cell markers (CalceinAM green/EthD-1red) was used as internal control. We used quantitative confluence (Essen), AnnexinV-PE staining (Accuri C6), expression of cl-caspase3, Cl-PARP and mitochondrial potential (TMRE-A) as validation criteria in A2780 and OVK18 cells following drug treatment which decreased proliferation, & increased apoptotic signaling with mitochondrial depolarization. Treatment blocked cytoplasmic MitoViewBlue staining while increased both nuclear NucView488-Casp3 substrate and red membranous CF594 AnnexinV staining. Merged images showed 100% mutual exclusivity between MitoViewBlue and caspase3 or AnnexinV stains in control and treated cells as determined by overlap and colocalization coefficients. Caspase3 and AnnexinV staining in treated cells were both separate and overlapped (yellow fluorescence) indicating the sequence of apoptotic-events. The protocol will help in deciphering mechanistic involvement of different stages/features of apoptosis in tumor cell following anti-cancer drugs in real-time.

Stability of the Distribution of Patient Health Questionnaire-9 Scores Against Age in the General Population: Data From the National Health and Nutrition Examination Survey.

Background: Epidemiological studies using the nine-item Patient Health Questionnaire (PHQ-9) have reported inconsistencies regarding the relationship between age and total scores. To determine whether this discrepancy is due to the stability of the distribution of PHQ-9 total scores against age, we investigated whether the total score distribution remains stable during adulthood, and also investigated the mathematical patterns of the total score distribution.Methods: The present study utilized data from 15,847 participants of the 2009–2014 United States National Health and Nutrition Examination Survey, all of whom responded to all PHQ-9 items. The stability of the total score distribution among different age groups was examined using overlap coefficients and graphical analysis.Results: High overlap coefficients were observed between all age groups for the distributions of PHQ-9 total scores, suggesting that the distribution of PHQ-9 total scores remains stable against age. Graphical analysis demonstrated that distributions of PHQ-9 total scores were similar across age groups. In addition, distributions of PHQ-9 total scores exhibited an exponential pattern, except at the lower end of the distribution.Conclusions: Our findings indicate that the stability of the distribution of PHQ-9 total scores throughout adulthood may underlie inconsistencies in the evidence regarding age-related changes in total depression scores.

Accuracy of tumor segmentation from multi-parametric prostate MRI and 18F-choline PET/CT for focal prostate cancer therapy applications

BackgroundThe study aims to assess the accuracy of multi-parametric prostate MRI (mpMRI) and 18F-choline PET/CT in tumor segmentation for clinically significant prostate cancer. 18F-choline PET/CT and 3 T mpMRI were performed in 10 prospective subjects prior to prostatectomy. All subjects had a single biopsy-confirmed focus of Gleason ≥ 3+4 cancer. Two radiologists (readers 1 and 2) determined tumor boundaries based on in vivo mpMRI sequences, with clinical and pathologic data available. 18F-choline PET data were co-registered to T2-weighted 3D sequences and a semi-automatic segmentation routine was used to define tumor volumes. Registration of whole-mount surgical pathology to in vivo imaging was conducted utilizing two ex vivo prostate specimen MRIs, followed by gross sectioning of the specimens within a custom-made 3D-printed plastic mold. Overlap and similarity coefficients of manual segmentations (seg1, seg2) and 18F-choline-based segmented lesions (seg3) were compared to the pathologic reference standard.ResultsAll segmentation methods greatly underestimated the true tumor volumes. Human readers (seg1, seg2) and the PET-based segmentation (seg3) underestimated an average of 79, 80, and 58% of the tumor volumes, respectively. Combining segmentation volumes (union of seg1, seg2, seg3 = seg4) decreased the mean underestimated tumor volume to 42% of the true tumor volume. When using the combined segmentation with 5 mm contour expansion, the mean underestimated tumor volume was significantly reduced to 0.03 ± 0.05 mL (2.04 ± 2.84%). Substantial safety margins up to 11–15 mm were needed to include all tumors when the initial segmentation boundaries were drawn by human readers or the semi-automated 18F-choline segmentation tool. Combining MR-based human segmentations with the metabolic information based on 18F-choline PET reduced the necessary safety margin to a maximum of 9 mm to cover all tumors entirely.ConclusionsTo improve the outcome of focal therapies for significant prostate cancer, it is imperative to recognize the full extent of the underestimation of tumor volumes by mpMRI. Combining metabolic information from 18F-choline with MRI-based segmentation can improve tumor coverage. However, this approach requires confirmation in further clinical studies.

Overlap coefficients based on Kullback-Leibler divergence: Exponential populations case

This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefficients, namely: Matusita’s measure ρ, Morisita’s measure λ and Weitzman’s measure ∆. A new overlap measure Λ based on Kullback-Leibler measure is proposed. The invariance property and a method of statistical inference of these coefficients also are presented. Taylor series approximation are used to construct confidence intervals for the overlap measures. The bias and mean square error properties of the estimators are studied through a simulation study.

Double trace interfaces

We introduce and study renormalization group interfaces between two holographic conformal theories which are related by deformation by a scalar double trace operator. At leading order in the 1/N expansion, we derive expressions for the two point correlation functions of the scalar, as well as the spectrum of operators living on the interface. We also compute the interface contribution to the sphere partition function, which in two dimensions gives the boundary g factor. Checks of our proposal include reproducing the g factor and some defect overlap coefficients of Gaiotto’s RG interfaces at large N , and the two-point correlation function whenever conformal perturbation theory is valid.

Similar coefficient for cluster of probability density functions

ABSTRACTIn this article, we propose a new criterion to evaluate the similarity of probability density functions (pdfs). We call this the criterion on similar coefficient of cluster (SCC) and use it as a tool to deal with overlap coefficients of pdfs in normal standard on [0;1]. With the support of the self-update algorithm for determining the suitable number of clusters, SCC then becomes a criterion to establish the corresponding cluster for pdfs. Moreover, some results on determination of SCC in case of two and more than two pdfs as well as relations of different SCCs and other measures are presented. The numerical examples in both synthetic data and real data are given not only to illustrate the suitability of proposed theories and algorithms but also to demonstrate the applicability and innovation of the proposed algorithm.

The q-Onsager algebra and multivariable q-special functions

Two sets of mutually commuting q-difference operators xi and yj, such that xi and yi generate a homomorphic image of the q-Onsager algebra for each i are introduced. The common polynomial eigenfunctions of each set are found to be entangled product of elementary Pochhammer functions in N variables and parameters. Under certain conditions on the parameters, they form two ‘dual’ bases of polynomials in N variables. The action of each operator with respect to its dual basis is block tridiagonal. The overlap coefficients between the two dual bases are expressed as entangled products of q-Racah polynomials and satisfy an orthogonality relation. The overlap coefficients between either one of these bases and the multivariable monomial basis are also considered. One obtains in this case entangled products of dual q-Krawtchouk polynomials. Finally, the ‘split’ basis in which the two families of operators act as block bidiagonal matrices is also provided.

Auto-Context Convolutional Neural Network (Auto-Net) for Brain Extraction in Magnetic Resonance Imaging.

Brain extraction or whole brain segmentation is an important first step in many of the neuroimage analysis pipelines. The accuracy and the robustness of brain extraction, therefore, are crucial for the accuracy of the entire brain analysis process. The state-of-the-art brain extraction techniques rely heavily on the accuracy of alignment or registration between brain atlases and query brain anatomy, and/or make assumptions about the image geometry, and therefore have limited success when these assumptions do not hold or image registration fails. With the aim of designing an accurate, learning-based, geometry-independent, and registration-free brain extraction tool, in this paper, we present a technique based on an auto-context convolutional neural network (CNN), in which intrinsic local and global image features are learned through 2-D patches of different window sizes. We consider two different architectures: 1) a voxelwise approach based on three parallel 2-D convolutional pathways for three different directions (axial, coronal, and sagittal) that implicitly learn 3-D image information without the need for computationally expensive 3-D convolutions and 2) a fully convolutional network based on the U-net architecture. Posterior probability maps generated by the networks are used iteratively as context information along with the original image patches to learn the local shape and connectedness of the brain to extract it from non-brain tissue. The brain extraction results we have obtained from our CNNs are superior to the recently reported results in the literature on two publicly available benchmark data sets, namely, LPBA40 and OASIS, in which we obtained the Dice overlap coefficients of 97.73% and 97.62%, respectively. Significant improvement was achieved via our auto-context algorithm. Furthermore, we evaluated the performance of our algorithm in the challenging problem of extracting arbitrarily oriented fetal brains in reconstructed fetal brain magnetic resonance imaging (MRI) data sets. In this application, our voxelwise auto-context CNN performed much better than the other methods (Dice coefficient: 95.97%), where the other methods performed poorly due to the non-standard orientation and geometry of the fetal brain in MRI. Through training, our method can provide accurate brain extraction in challenging applications. This, in turn, may reduce the problems associated with image registration in segmentation tasks.

Tridiagonalization and the Heun equation

It is shown that the tridiagonalization of the hypergeometric operator L yields the generic Heun operator M. The algebra generated by the operators L, M and Z = [L, M] is quadratic and a one-parameter generalization of the Racah algebra. The Racah-Heun orthogonal polynomials are introduced as overlap coefficients between the eigenfunctions of the operators L and M. An interpretation in terms of the Racah problem for su(1,1) and separation of variables in a superintegrable system are discussed.

Machine learning in a graph framework for subcortical segmentation.

Automated and reliable segmentation of subcortical structures from human brain magnetic resonance images is of great importance for volumetric and shape analyses in quantitative neuroimaging studies. However, poor boundary contrast and variable shape of these structures make the automated segmentation a tough task. We propose a 3D graph-based machine learning method, called LOGISMOS-RF, to segment the caudate and the putamen from brain MRI scans in a robust and accurate way. An atlas-based tissue classification and bias-field correction method is applied to the images to generate an initial segmentation for each structure. Then a 3D graph framework is utilized to construct a geometric graph for each initial segmentation. A locally trained random forest classifier is used to assign a cost to each graph node. The max-flow algorithm is applied to solve the segmentation problem. Evaluation was performed on a dataset of T1-weighted MRI's of 62 subjects, with 42 images used for training and 20 images for testing. For comparison, FreeSurfer and FSL approaches were also evaluated using the same dataset. Dice overlap coefficients and surface-to-surfaces distances between the automated segmentation and expert manual segmentations indicate the results of our method are statistically significantly more accurate than the other two methods, for both the caudate (Dice: 0.89 ± 0.03) and the putamen (0.89 ± 0.03).

Voxel Placement Precision for GABA-Edited Magnetic Resonance Spectroscopy.

The purpose of the present study was to assess the reproducibility of voxel placement for GABA-edited MRS. GABA-edited MRS data were acquired in 13 healthy volunteers from (3 cm)3 voxel; and within the same session a second acquisition was independently prescribed. A three-dimensional voxel mask image was reconstructed in T1-image-space using the SVMask tool (in house software). Reproducibility of voxel placement was assessed using the Dice overlap coefficient, both within-subject and between-subject following co-registration of T1 images and transformation of voxel mask images to standard space. Within-subject overlap coefficients were 86% ± 5%. Between-subject overlap coefficients were 75% ± 10%. For the two voxel locations considered (occipital and sensorimotor), voxel overlap was very similar. Between-subject values are higher due to between-session effects, anatomical variability and volume mismatch in standard space. While surprisingly low in terms of volume overlap, the overlap coefficients correspond to acceptable linear displacements.